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A 3 cm×3 cm3cm×3cmstart color #1fab54, 3, start text, c, m, end text, times, 3, start text, c, m, end text, end color #1fab54 rectangle sits inside a circle with radius of 4 cm4cmstart color #11accd, 4, start text, c, m, end text, end color #11accd.What is the area of the shaded region? Round your final answer to the nearest hundredth.

A 3 cm3 cm3cm3cmstart color 1fab54 3 start text c m end text times 3 start text c m end text end color 1fab54 rectangle sits inside a circle with radius of 4 cm class=

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The areas of the circle and rectangle are

[tex]\begin{gathered} A_{\text{circle}}=r^2\cdot\pi=\pi(4)^2=16\pi \\ \text{and} \\ A_{\text{rectangle}}=lw=3\cdot3=9 \end{gathered}[/tex]

Therefore, the area of the shaded region is

[tex]\Rightarrow A_{\text{shaded}}=A_{circle}-A_{\text{rectangle}}=16\pi-9=_{}41.2654\ldots\approx41.27[/tex]

The rounded answer is 41.27cm^2

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